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In this paper, the vibration of an Euler-Bernoulli functionally graded beam under a moving oscillator is investigated. The beam is considered to be simply supported whereas its material composition is varying along the thickness according to a power law. Furthermore, the internal damping of the beam is modeled by viscoelastic fractional Kelvin-Voigt model which is described by Caputo-Fabrizio definition. The governing equations are solved by the decomposition method coupled with Laplace transforms. Three comparison studies were conducted and good agreements were obtained. The results clearly indicate the advantages of using Caputo-Fabrizio fractional derivative model. Also it is observed that the oscillator velocity, the material grading order, the damping ratio, and the fractional derivative order have significant effects on the dynamic response of the beam.
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